Sun search method and apparatus for a satellite stabilized in three axes

ABSTRACT

The sun search method for a satellite stabilized in three axes according to the invention uses a sun sensor device with a visual field possibly containing gaps, and a rotational speed gyro which measures in a measuring axis that is oriented arbitrarily. A regulating law with the form τ=-kGG T  ω is used (τ=regulating torque, k=amplification factor, G=directional vector of measuring axis of rotational speed gyro, ω=rotational speed vector of the satellite). A rotational wheel momentum H which is not parallel to the measuring axis, is generated with the aid of an additional flywheel device.

BACKGROUND AND SUMMARY OF THE INVENTION

The invention relates to a sun search method and apparatus for asatellite which is stabilized in three axes.

International patent document WO 93/04923 A1 discloses a measuringdevice of this generic type for use in attitude regulation of asatellite stabilized in three axes, and a method for acquiring the sunfrom any initial attitude of the satellite in which the sun is notwithin the visual field of the sun sensors. This measuring systemcomprises sun sensors to determine the direction of the sun relative toa coordinate system which is integral with the satellite as well as arotational speed gyro which measures on one axis. The visual fieldand/or measuring range of the sun sensors must cover the full angle of2π in a preselectable plane of the coordinate system, and only onelimited angle range less than π/2 in both directions orthogonal thereto.The permissible direction of the measuring axis of the rotational speedgyro is thus subject to a limitation that depends on the width of thevisual field of the sun sensors orthogonal to the preselectable plane.The conditions specified for the angles α₁ and α₂ that define the visualfield of the sun sensors in the preselectable plane and orthogonalthereto, and for the permissible range of angle β measured between themeasuring axis of the rotational speed gyro and the preselectable planeare defined therein as follows:

    0≦α≦2π                              (1a)

    -α.sub.2max ≦α.sub.2 ≦α.sub.2max( 1b)

    |β|≧(π/2) -α.sub.2max( 1c)

The XZ plane of the satellite-integral coordinate system is preferred asthe preselectable plane that must be completely covered by the visualfield of the sun sensor system, with the Z axis being oriented to thecenter of the earth as the yaw axis in the case of a geostationary earthsatellite for example, the X axis aligned in the direction of the orbitas the roll axis, and the Y axis, being orthogonal to the other twoaxes, as the pitch axis.

However, it may happen that because of the requirements imposed by otheroperational maneuvers, the above condition relative to the direction ofthe measuring axis of the rotational speed gyro can no longer befulfilled; i.e.,

    β.sub.max ≦(π/2) -α.sub.2max,         (2)

In addition, the above requirement that the visual field of the sunsensor system in the preselectable plane must include the full angle of2π constitutes a limitation that cannot always be allowed. Also, it isalso not optimal for cost reasons, since a corresponding number of sunsensors must be provided to cover the entire angle range of 2π. Inaddition, if one or more sun sensors should fail, gaps will occur in thevisual field, resulting in the provided measurement and evaluationmethod and in particular the provided sun acquisition method no longerbeing operable. The same is true also if the all-around visual field isrestricted by projecting antennas or other devices mounted on thesatellite.

The goal of the present invention is to provide a method and apparatusof the species recited at the outset for sun acquisition for a satellitestabilized in three axes, that functions even when the limitationsdefined above regarding the sun sensor visual field as well as thedirection of the measuring axis of the rotational speed gyro can nolonger be maintained.

Another object is to provide a method and apparatus for sun acquisitionwhich is usable even when the visual field of the sun sensor system hasgaps in the plane and the above-mentioned measuring axis is orientedarbitrarily with respect to this visual field.

Finally, still another object of the invention is to provide a satellitestabilized in three axes which utilizes the sun search method andapparatus according to the invention.

The goal regarding the sun search method is achieved by the sunacquisition method and apparatus according to the invention, in which aflywheel device is used to generate a momentum whose correspondingmomentum vector H need not be oriented parallel to the direction of themeasuring axis of the rotational speed gyro. The use of a knownregulating procedure (e.g., WO 93/04923 A1) is assumed in thisconnection, making the rotational speed component oriented parallel tothe measuring axis of the rotational speed gyro equal to zero.Generation of the additional momentum means that as a result of theregulating process, merely a rotation of the satellite around themomentum axis remains. This revolution will in a great many casessuffice for the sun to appear in the visual field of the sun sensorsystem.

In an advantageous embodiment of the invention, the visual field of thesun sensor system continuously covers an angle of at least π in thepreselectable plane, while in another embodiment, the visual field hasone or more sectors interrupted by gaps, none of which covers an angleof π.

According to the invention, a satellite can be stabilized in three axeswithout the limitations recited at the outset regarding its sun sensorsystem as well as the direction of the measuring axis of its rotationalspeed gyro, measuring on one axis. In other words there is no longerall-around visibility of the sun sensor system in the preselectableplane, and the single measuring axis of the rotational speed gyro can beoriented as desired. The important feature is the addition of a flywheeldevice capable of generating momentum components around all threecoordinate axes. Such a satellite with only one uniaxially measuringrotational speed gyro when the sun sensor visual field is sharplyrestricted for rotational speed measurement, could not have beendesigned earlier because of the problem that a sun search must becommenced from an unknown initial attitude. The problem could be solvedin the past only when a rotational speed gyro was available thatmeasured on three axes and, especially in the case of a redundantdesign, was correspondingly expensive and delicate. In contrast, in themethod and apparatus according to the invention, a satellite uses auniaxially measuring rotational speed gyro for the essential sun searchmaneuver, which is made possible by the flywheel device that isprovided.

Objects, advantages and novel features of the present invention willbecome apparent from the following detailed description of the inventionwhen considered in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic illustration of the visual field of a sunsensor in a prior art system;

FIG. 2 is a diagrammatic illustration of the visual field in the XZplane of a system which fails to satisfy the requirements according tothe prior art;

FIG. 3 is a schematic depiction of a flywheel arrangement according tothe invention;

FIG. 4 is a block diagram of an observer arrangement for generatingpositioning signals to perform the process according to the invention;and

FIG. 5 is a flow diagram which illustrates the steps of the process fordifferent sun sensor configuration and initial rates according to theinvention.

DETAILED DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the position and size of the required visual field of thesun sensor system according to the prior art, as well as the permissiblealignment of the measuring axis (directional vector G) of the uniaxiallymeasuring gyro in a satellite-integral coordinate system XYZ. The sunsensor system has all-around visibility (0≦α₁ ≦2π) in the XZ plane, andthe visual field is limited to ±α_(2max) in both directions orthogonalthereto, so that an area in the shape of a double cone exists around thepositive and negative Y axis, which the sun sensor system does notinclude. Only the two areas shown shaded are permitted for thedirectional vector G of the rotational speed gyro, and they arecharacterized by the requirement:

    |β|≧(π/2) -α.sub.2max.(1c)

Here β represents the angle between the XZ plane and the directionalvector G. This requirement cannot always be met, however, because of therequirements imposed by other operational maneuvers. In this case theprior art method provided for sun searching likewise can no longer beused.

This is also true when the sun sensor system no longer has all-aroundvisibility, as for example in the event of failure of a single sunsensor (which, when reliably functioning covers a portion, for exampleone-third, of the 360° visual field), or when a number of individual sunsensors sufficient for all-around visibility must be omitted for costreasons.

A system in which the above conditions are violated occurs for examplewhen the sun sensor visual field covers an angle that is only slightlygreater than π in the XZ plane of the satellite-integral coordinatesystem, and the direction vector G of the uniaxially measuringrotational speed gyro likewise lies in the XZ plane, preferably in themiddle of this visual field. Such an arrangement is shown schematicallyin FIG. 2, in which the visual field in the XZ plane is indicated byshading and is centered around the directional vector G of the measuringaxis of the rotational speed gyro. In particular, directional vector Gcan also coincide with the X axis. The visual field should include atleast the two vectors ±e_(R) defined as follows:

    e.sub.R =Ge.sub.Y                                          (3)

where e_(Y) is the unity vector in the direction of the Y axis. Ofcourse, the visual field of the sun sensor system so defined also has acertain portion orthogonal to the XZ plane, ±30° for example, with thesevalues permitted to decrease somewhat toward the edge.

A satellite stabilized in three axes with such a special system for thesun sensor visual field as well as the measuring axis of the rotationalspeed gyro has the usual torque generating device for the purpose ofattitude regulation, such device generally having three pairs ofattitude regulating jets, each of which can generate positive andnegative momentum around one of the coordinate axes. Instead of attituderegulating jets, other devices can be provided for generating momentum,a system of magnetic coils when an external magnetic field is presentfor example.

The system according to the present invention is additionally providedwith a torque generating device able to generate momentum components inall three coordinate directions. Preferably this is a flywheel devicewhich in the simplest case consists of a single flywheel pivotable inany desired direction. Generally, however, at least three separateflywheels are provided whose rotational axes need not all lie in thesame plane. By a suitable adjustment of the rotational speed androtational direction of these flywheels, it is then possible to producea resultant momentum (momentum vector H) with the desired value and inthe desired direction.

A preferred embodiment of such a flywheel device is shown in FIG. 3, inwhich two reaction wheels RWX and RWZ, whose rotational axes coincidewith the X and Z axes, respectively, as well as two twist wheels FMW1and FMW2 whose rotational axes each enclose the same angle δ relative tothe negative Y axis, but with opposite signs, and are coplanar with thisaxis. The corresponding plane forms angle η with the negative X axis.Typical numerical values for this angle are:

    η=45°

    δ=10°

Such a system of flywheels can also be defined as follows independentlyof the coordinate axes: Two twist wheels have rotational axes thatenclose an acute angle, while the two reaction wheels have theirrotational axes mounted orthogonally with respect to one another. Thetwo rotational axis planes spanned by the two rotational axes areorthogonal to one another, and the bisectors of the angles spanned bythe two wheel pairs respectively lie in a plane oriented orthogonally tothe two rotational axis planes. Twist wheels are generally designed todeliver a high momentum in one direction and to maintain it, whilereaction wheels can generate a relatively small momentum in bothrotational directions. The flywheel device in FIG. 3 is preferablydesigned to deliver a momentum vector H in the direction of the Y axis,so that any deviations that occur in the other two coordinate directionscan be easily adjusted. It is designed redundantly so that even if oneof the four flywheels should fail, it is still possible to generate amomentum vector H approximately not only in the direction of thenegative Y axis but in any other direction as well.

To perform the sun search with such a sensor system, when the rotationalspeed is known with a certain degree of accuracy (for example after thesatellite separates from the carrier rocket), rotation is initiallyslowed down under control in a known manner. For this purpose, with theaid of the above-mentioned torque generating device (for example theattitude regulating jets), a torque τ is created that is orientedopposite to the rotational speed vector ω that acts for the followingspace of time Δt:

    Δt=|Iω|/|τ|(4)

where I is the inertial sensor of the satellite. During this process,the flywheels of the flywheel system are at rest. Consequently, a smallunknown residual rotational speed ω_(R) will generally remain, to beeliminated in the following step.

The invention addresses this point, but it can also be used without themethod step described above. A constant momentum vector H is set withthe aid of the flywheel device. (The only requirement initiallyapplicable to the flywheel device is that it not be oriented parallel todirection vector G of the measuring axis of the rotational gyro.) Asalready mentioned, a regulator is also necessary which outputspositioning signals for the torque generating device based on themeasuring signals from the rotational speed gyro to create regulatingtorque. Such regulators are found in the attitude regulating device ofevery conventional satellite. Accordingly, a system equation is obtainedas follows, neglecting the Euler term:

    Iω(H-kGG.sup.T)ω                               (5)

where H is the cross product matrix of momentum vector H, k is anamplification factor, G^(T) is the vector transposed to G, and ω is thetime derivative of rotational speed vector ω. The second term on theright-hand side of this equation corresponds to the regulating lawalready known from International patent document WO 93/04923 A1, whichdamps the component of the rotational speed vector ω parallel todirectional vector G. The first term, which depends on momentum vectorH, causes a coupling of the rotational speed component orientedorthogonally to H with measuring axis G. Rotational energy is constantlydrawn from the rotation around the component of rotational speed vectorω oriented orthogonally to directional vector G and orthogonally tomomentum vector H and coupled into the directional axis, where it isthen subject to damping by the second term. This occurs with the aid ofthe attitude regulating system, for example by actuating the attituderegulating jets to generate regulating torque τ.

The component of the rotational speed vector ω oriented orthogonally todirectional vector G is damped when momentum vector H is set orthogonalto G. Then only a small rotation around H remains as a result of theregulating process, which can also be zero.

In general, the above system equation can also be formulated as followswith the aid of a system matrix A:

    ω=Aω.                                          (5a)

The choice of vectors H and G determines the eigenvalues of the systemmatrix A and hence the damping behavior. If these vectors are chosenother than according to the guideline that G and H should be orthogonalto one another, the rotational speed components are in fact regulated tozero around all three coordinate axes, but with highly oscillatorytransient response, which is normally undesirable.

The case that is especially relevant in practice, as shown in FIG. 2 aswell, is that in which G and H lie in the XZ plane and are orientedorthogonally to one another. With this configuration, the rotationalspeed components along directional axis G and the Y axis of thesatellite-integral coordinate system are completely damped, so that onlya rotation around momentum vector H remains, as mentioned above.

If the momentum vector H is oriented as shown in FIG. 2, namely at theedge of the visual field of the sun sensor system, which in all eventscovers at least angle π and then also includes vector H, a residualrotation of the satellite by H sooner or later necessarily leads toacquisition of the sun. If this residual speed is very low or even equalto zero, however, a search maneuver that consists in rotation around anaxis e_(R) is launched by actuating the torque generating device, inother words the attitude regulating jets for example. Such rotationoccurs in the XZ plane within the visual field of the sun sensor system,sufficiently close to the edge that this also applies to the vector-e_(R). Thus, e_(R) =H can be chosen as the preferred axis. Thisconstitutes the optimal case for use. The duration of the requiredmomentum pulses is estimated on the basis of the residual speed thatremains following regulating damping using the above regulating law.

When the visual field of the sun sensor system in the XZ plane consistsof one or more partial sectors separated from one another by gaps, noneof which sectors covers a comprehensive angle range of at least π, afterthe method step according to the invention is performed (i.e., regulateddamping using the above regulating law), a different final searchmaneuver is employed. This maneuver consists of a rotation of thesatellite around the rotational axis or successive rotations around aplurality of rotational axes being commanded after taking into accountthe orientation and size of the partial sectors, the direction of suchrotation ensuring that the sun eventually appears in one of the partialsectors. Such maneuvers are known for example from German patentdocument DE 27 49 868 C3 or the article "The Attitude and Orbit ControlSubsystem of the TV-SAT/TDFI Spacecraft," by H. Bittner et al., IFACSymposium on Automatic Control in Space, 1982, Pages 83 to 102. In thatmethod, however, a rotational speed gyro that measures on three axes oran equivalent measuring device is needed. In order to take into accountthe fact that in the present case a rotational speed gyro that measureson only one axis is available, a observer is used to estimate theunknown component of the rotational speed vector ω which is orientedorthogonally to directional vector G of the measuring axis. This canhave the structure shown in FIG. 4 for example.

The dynamics of the real satellite are shown in dashed box 1 and formthe equation

    ω=I.sup.-1 Hω+I.sup.-1 τ                   (6)

where τ is the control torque supplied to the satellite. An output valuey is determined by rotational speed gyro 2 that measures on one axis,said value being proportional to the rotational speed componentorthogonal to directional vector G of the measuring axis of therotational speed gyro:

    y˜G.sup.T ω.                                   (7)

Both a signal that corresponds to regulating momentum τ and the outputsignal y are supplied to observer 3 that simulates the satellitedynamics in detail. The observer generates a signal y from which theoutput signal y of the real satellite is subtracted in a summing point6. In the observer, the estimated values ω and their time derivative areformed as intermediate values. The value s usually represents theLaplace or differential operator. In addition, inertial matrix I of thesatellite is used.

In the system shown, observer 3 can be a hardware circuit or simply analgorithm in the on-board computer of the satellite.

The differential value formed in summing point 6 can optionally passthrough an amplifier 7 in which a vectorial amplification factor l withl^(T) =(l₁, l₂, l₃) is used. The estimated value ω formed in theobserver which contains three estimated components in all threecoordinate directions is sent to a regulator 4 that generatespositioning signals for a downstream torque generating device 5 in suchfashion that the following regulating law is implemented:

    τ=k.sub.D (ω.sub.R -ω).                    (8)

Hence such regulation causes estimated value ω to be corrected toreference vector ω_(R), where ω_(R) is the rotational speed vector to beachieved for searching for the sun. This vector, taking into account thesize and orientation of the visual fields of the individual sun sensors,must be designed and possibly changed continuously in a plurality ofsuccessive steps to assure that the sun finally appears in one of thepartial sectors.

It is important to keep in mind in this connection that even during thisfinal search maneuver using the flywheel device according to theinvention, a momentum vector H must be applied, oriented in such fashionthat the observability matrix Q_(B) assigned to the observer has a rankof 3. As is known, this matrix is given by: ##EQU1##

Observability exists as soon as the three line vectors of this matrixare linearly independent of one another. This can be accomplished e.g.,by adjusting momentum vector H in such fashion that an angle of 45° isspanned between H and G. As a result, all three motion axes are coupledwith one another.

The prerequisite for the use of this search method is that thesatellite, following completion of regulator damping, rotates only at aspeed so low that the following inequality is fulfilled:

    |Iω|<<|H|.       (10)

Then the nonlinear influence of Euler term ωIω is negligible in thefollowing equation of motion:

    ω+ω(ω+H)=τ                           (11)

and the above-mentioned observer equation results. This assumptionhowever is always made after completion of regulated damping accordingto the invention. In the case of a spherical mass distribution in thesatellite, the Euler term ωIω disappears even when the rotational speeds|ω| are high.

Finally, for different cases (sun sensor field of view, initial rates)FIG. 5 shows in a comprehensive representation the individual partialsteps of the search strategy for sun seeking according to the invention.If the initial rate is approximately known then in step 502 a forwarddamping of ω is performed by means of torque pulses. If on the otherhand ω is not known, or after the damping in step 502 if applicable, awheel angular momentum adjustment is performed in step 503 in order toadjust H and G so that they are orthogonal to each other. Thereafter, instep 504 the control law τ=-kGG^(T) ω is applied. Next, if the sunsensor visual field is at least equal to an angle of π radians, then thesatellite is rotated in step 506 according to the vector equation e_(R)(=H). If, on the other hand, the sun sensor configuration is such thatthe sun sensor visual field is smaller than π, then in step 507, anadjustment of the wheel angular momentum is performed according to RankQ_(B) =3. Finally in step 508 a search strategy of prior art isperformed based on the angular rate estimates delivered by the observer.

Although the invention has been described and illustrated in detail, itis to be clearly understood that the same is by way of illustration andexample, and is not to be taken by way of limitation. The spirit andscope of the present invention are to be limited only by the terms ofthe appended claims.

What is claimed is:
 1. Method for sun seeking for a satellite stabilized in three axes, by means of a system havinga sun sensor device whose visual field covers one or more partial sectors, separated from one another by gaps, of a preselectable plane of a satellite-integral orthogonal three-axis coordinate system and an area orthogonal to this plane; a rotational speed gyro which measures uniaxially with a measuring axis oriented arbitrarily; a first torque generating device other than a flywheel device, for generating torque around all three coordinate axes; and a regulator which, based on the measuring signals of the rotational speed gyro for purposes of generating regulating torque, outputs positioning signals for the first torque generating device, based on regulating process of the following form: τ=-kGG^(T) ω and where τ is a regulating torque, k is an amplification factor, G is the directional vector of the measuring axis with |G|=1, G^(T) being the vector transposed to G, and ω is the rotational speed vector of the satellite, said method comprising: providing a second torque generating device in the form of a flywheel arrangement on said satellite; and said flywheel arrangement generating a rotation wheel momentum having a momentum vector H that is not parallel to the direction of the measuring axis.
 2. Method according to claim 1 wherein:said sun sensor device has a visual field which covers an angle range of at least π continuously within the preselectable plane; and the momentum vector H is generated in a direction which is oriented orthogonally to directional vector G of the measuring axis.
 3. Method according to claim 1 further comprising:adjusting orientation of momentum vector H so that both H and also -H, starting from the origin of the coordinates of the satellite-integral coordinate system, lie within the visual field of the sun sensor system.
 4. Method according to claim 3 further comprising:in the event that rotation of the satellite around the direction of momentum vector H after application of the regulating process is small or zero, causing a rotation around a vector e_(R) which is chosen so that it lies, together with a vector -e_(R), in the preselectable plane within the visual field of the sun sensor system.
 5. Method according to claim 4 wherein vector e_(R) is collinear with momentum vector H.
 6. Method according to claim 1 wherein:sun sensor device has a visual field within the preselectable plane that does not have a partial sector that continuously covers an angle range of at least π; and momentum vector H is oriented in such fashion that matrix: ##EQU2## has a rank of
 3. 7. Method according to claim 6 wherein momentum vector H encloses an angle of 45° with measuring axis G.
 8. Method according to claim 6 further comprising:causing at least a rotation of the satellite around at least one rotational axis, taking into account the orientation and value of the partial sectors of the visual field of the sun sensor system, the direction of such at least one rotation ensuring that the sun will eventually appear in one of the partial sectors; using an observer to estimate an unknown component of the rotational speed vector ω oriented orthogonally to measuring axis (R).
 9. A sun acquisition device for a satellite which is stabilized in three axes, comprising:a sun sensor system having a visual field that covers one or more partial sectors separated from one another by gaps within a preselectable plane in a satellite-integral, three-axis, orthogonal system of coordinates; a uniaxially measuring rotational speed gyro having an arbitrarily oriented measuring axis; a torque generating device that generates torques around all three axes; a regulator which, based on the measuring signals of the rotational speed gyro for purposes of generating regulating torque, outputs positioning signals for the torque generating device, based on regulating process of the following form: τ=-kGG^(T) ω, where τ is a regulating torque, k is an amplification factor, G is the directional vector of the measuring axis with |G|=1, G^(T) being the vector transposed to G, and ω is the rotational speed vector of the satellite; and a flywheel arrangement that is able to generate momentum components around all three coordinate axes; said flywheel arrangement generating a rotation wheel momentum having a momentum vector H that is not parallel to the direction of the measure axis.
 10. Satellite according to claim 9 wherein the flywheel arrangement comprises at least three flywheels with rotational axes that do not all lie in a single plane.
 11. Satellite according to claim 10 further comprising:least one reaction wheel; and one twist wheel.
 12. Satellite according to claim 11 further comprising:at least two twist wheels with rotational axes enclosing an acute angle; and at least two reaction wheels arranged orthogonally to one another with respect to their rotational axes; wherein the two rotational axis planes spanned by two rotational axes are orthogonal to one another; and bisectors of the angles spanned by the two wheel pairs lying in a plane are oriented orthogonally to the two rotational axis planes.
 13. A method for sun seeking for a satellite which is stabilized about plural axes by means of a sun sensor whose visual field covers at least two partial sectors separated from one another by gaps, at least a first torque generating device for generating torques around said plural axes, and a rotational speed gyro which measures rotational speed about an arbitrarily selected measuring axis, said method comprising:providing a second torque generating device in the form of a flywheel arrangement on said satellite; and said flywheel arrangement generating a rotational wheel momentum having a momentum vector H that is not parallel to measuring axis of said rotational speed gyro, whereby said satellite rotates about an axis of the momentum vector H. 